The fourth Test is schedule to start on January 15.
The staging of fourth Test between Australia and India at the Gabba was under dark clouds after the visiting team had expressed reluctance to undergo another round of hard quarantine and an instant city-wide lockdown due to new COVID-19 cases.
But with the stay-at-home orders lifted on Monday, Hockley said the Test will be held as scheduled.
"The fourth Test will be at the Gabba, as planned," he told commercial radio SEN. "On the basis of yesterday's discussions we are full steam ahead to play the fourth Test at the Gabba and really looking forward to it."
Hockley said he had a world with Queensland state health officials and BCCI secretary to receive the green light.
"I had a call last night from the BCCI secretary, very late last night, and he confirmed we are good to travel to Brisbane on Tuesday," Hockley said.
"We're extremely grateful for their support," he said of the Indian side.
Hockley also stated that CA had made arrangement of a charter plane for the players, who will stay in a Brisbane hotel retained "exclusively" for their use.
Meanwhile, Queensland Premier Annastacia Palaszczuk has also assured that the Brisbane Test would take place but with restrictions on crowd numbers.
"The Gabba will be filled to half the capacity and masks are mandatory for entering and for leaving and moving around the stadium," she said.
The series has been hit by several virus-related problems, with spectator numbers severely limited in the ongoing Sydney Test due to COVID-19 cluster in the city.
The Boxing Test in Melbourne was declared a possible Covid-19 hotspot, and five Indian players were alleged to have violated the bio-security protocol by dining at a restaurant in the city.
(With AFP inputs)